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Carnegie Mellon Center for Nonlinear Analysis


Optimal Transport for the System of Isentropic Euler Equation

Michael Westdickenberg
Georgia Institute of Technology
School of Mathematics

Abstract: The isentropic Euler equations form a system of conservation laws modeling compressible fluid flows with constant thermodynamical entropy. Due to the occurrence of shock discontinuities, the total energy of the system is decreasing in time. We review the second order calculus on the wasserstein space of probability measures and show how the isentropic Euler equations can be interpreted as a steepest descent equation in this framework. We introduce a variational time discretization based on a sequence of minimization problems, and show that this approximation converges to a suitably defined measure-valued solution of the conservation law. Finally, we present some preliminary results about the numerical implementation of our time discretization.